Review of Semileptonic $B$ Anomalies

Abstract

We review the current status and implications of the anomalies (i.e. deviations from the Standard Model predictions) in semi-leptonic $B$ meson decays, both in the charged and in the neutral current. In $b\to s{\ell }^{+}{\ell }^{-}$ transitions significant tensions between measurements and the Standard Model predictions exist. They are most pronounced in the branching ratios ${\mathcal{B}}_{B\to K{\mu }^{+}{\mu }^{-}}$ and ${\mathcal{B}}_{B_s\to \varphi {\mu }^{+}{\mu }^{-}}$ (albeit quite dependent on the form factors used) as well as in angular observables in $B\to K^{\ast }{\mu }^{+}{\mu }^{-}$ (the $P_5^{\prime }$ anomaly). Because the measurements of ${\mathcal{B}}_{B_s\to {\mu }^{+}{\mu }^{-}}$ and of the ratios $R_K$ and $R_{K^{\ast }}$ agree reasonably well with the SM predictions, this points towards (dominantly) lepton flavour universal New Physics coupling vectorially to leptons, i.e. contributions to $C_9^{\mathrm{U}}$. In fact, global fits prefer this scenario over the SM hypothesis by $5.8\sigma$. Concerning $b\to c\tau \nu$ transitions, $R(D)$ and $R(D^{\ast })$ suggest constructive New Physics at the level of $10\%$ (w.r.t. the Standard Model amplitude) with a significance above $3\sigma$. We discuss New Physics explanations of both anomalies separately as well as possible combined explanations. In particular, a left-handed vector current solution to $R(D^{(\ast )})$, either via the $U_1$ leptoquark or the combination of the scalar leptoquarks $S_1$ and $S_3$, leads to an effect in $C_9^{\mathrm{U}}$ via an off-shell penguin with the right sign and magnitude and a combined significance (including a tree-level effect resulting in $C_{9\mu }^{\mathrm{V}}=-C_{10\mu }^{\mathrm{V}}$ and $R(D^{(\ast )})$) of $6.3\sigma$. Such a scenario can be tested with $b\to s{\tau }^{+}{\tau }^{-}$ decays. Finally, we point out an interesting possible correlation of $R(D^{(\ast )})$ with non-leptonic $B$ anomalies.

Invited review for EPJST. 24 pages, 5 figures. Incorporated a footnote on page 3, introducing the newly included Ref. [33]. Additionally, added a note following the acknowledgments section on a newly released experimental analysis

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